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A Hosszu-Gluskin Algebra and a Central Operation of (sm, m)-Groups

In this paper we prove a generalization of the Hosszu-Gluskin theorem for ( ´ sm, m)-groups in terms of a {; ; ; 1, (s − 1)m + 1}; ; ; -neutral operation and we define the algebra  Qm, n ·, ϕ, c m 1 o associated to the (sm, m)-group (Q, A). The central operation of an (n, m)-group is defined in [7]. Research results of central operation properties using a bijection σα : Qm → Qm are presented by means of a series of theorems. Then, a central operation of an (sm, m)-group is investigated using the previously mentioned algebra.

(n ; m)-group ; {; ; ; 1 ; n-m+1}; ; ; -neutral operation ; central operation

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